How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm

Solution:

Given, a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

We have to find the number of spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece.

Volume of cuboid = length × width × height

Volume of solid rectangle = 66 × 42 × 21

= 58212 cm³

Volume of sphere = (4/3)πr³

Given, diameter of spherical lead shots = 4.2 cm

Radius = 4.2/2 = 2.1 cm

Volume of spherical lead shots = (4/3)(22/7)(2.1)³

= (4/3)(22)(0.3)(2.1)²

= (4)(22)(0.1)(2.1)²

= 38.808 cm³

Number of spherical lead shots that can be obtained = volume of rectangular lead piece/volume of spherical lead shots.

= 58212/38.808

= 1500

Therefore, 1500 spherical lead shots can be obtained from the rectangular lead piece.

✦ Try This: How many shots each having diameter 3 cm can be made from a cuboidal lead solid of dimensions 11 cm x 12 cm x 14 cm?

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.3 Problem 11

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm

Summary:

1500 spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm

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